They're sort of right. Domiciliary carers can assist with medications, provided they've had appropriate training and the care provision contract allows for it. However in reality this usually means little more than popping tablets out of the blister pack and placing them within reach of the client.
In order to administer medications, carers need to have a specific medicines management qualification (which many do have) because of the regulatory controls involved in administering and recording of controlled drugs and medicines.
Not all care companies offer medication administration, and the ones that do will probably charge extra for it. Administering meds means the company loses some flexibility in that their visits will have to be on time (rather than just within a time window) and they have to commit specific carers who hold the correct qualifications. So their costs are higher.
Might be worth a chat with Adult Social Care to see if the service is available in your area, and if those arrangements could be put in place for your wife?